The period of time for which eggs, sperm and embryos can be frozen could be extended, as the government calls for views on the current 10-year limit.
It said women's choices on when to have children were being restricted, despite advances in freezing technology.
Only the eggs of people whose fertility may be affected by disease can be kept for longer - up to 55 years.
The regulator said the time was right to consider a "more appropriate" storage limit.
So the government has now launched a consultation on the current law.